Browsing Department of Mathematics and Statistics: Dr. Andrew D. Lewis by Author "Lewis, Andrew D."
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Affine connection control systems
Lewis, Andrew D. (1999)The affine connection formalism provides a useful framework for the investigation of a large class of mechanical systems. Mechanical systems with kinetic energy Lagrangians and possibly with nonholonomic constraints are ... 
Affine connections and distributions
Lewis, Andrew D. (1996)We investigate various aspects of the interplay of an affine connection with a distribution. When the affine connection restricts to the distribution, we discuss torsion, curvature, and holonomy of the affine connection. ... 
Aspects of Geometric Mechanics and Control of Mechanical Systems
Lewis, Andrew D. (1995)Many interesting control systems are mechanical control systems. In spite of this, there has not been much effort to develop methods which use the special structure of mechanical systems to obtain analysis tools which ... 
Configuration controllability of simple mechanical control systems
Lewis, Andrew D.; Murray, Richard M. (Society for Industrial and Applied Mathematics, 1995)In this paper we present a definition of "configuration controllability" for mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential energy. A computable test for this ... 
Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups
Bullo, Francesco; Leonard, Naomi E.; Lewis, Andrew D. (IEEE, 2000)In this paper, we provide controllability tests and motion control algorithms for underactuated mechanical control systems on Lie groups with Lagrangian equal to kinetic energy. Examples include satellite and underwater ... 
Controllability of a hovercraft model (and two general results)
Lewis, Andrew D.; Tyner, David R. (2003)Modelling and controllability studies of a hovercraft system are undertaken. The system studied is a little more complicated than some in the literature in that the inertial dynamics of the thrust fan are taken into ... 
Controllable kinematic reductions for mechanical systems: concepts, computational tools, and examples
Bullo, Francesco; Lewis, Andrew D.; Lynch, Kevin M. (2001)This paper introduces the novel notion of kinematic reductions for mechanical systems and studies their controllability properties. We focus on the class of simple mechanical control systems with constraints and model ... 
Decompositions of control systems on manifolds with an affine connection
Lewis, Andrew D.; Murray, Richard M. (NorthHolland, 1997)In this letter we present a decomposition for control systems whose drift vector field is the geodesic spray associated with an affine connection. With the geometric insight gained with this decomposition, we are able to ... 
Discussion on: ``Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty''
Lewis, Andrew D. (Lavoisier, 2005)This is an invited discussion paper on the paper ``Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty'' by XingGang Yan, Sarah K. Spurgeon, and Christopher Edwards, that will appear in the ... 
Energypreserving affine connections
Lewis, Andrew D. (1997)A Riemannian affine connection on a Riemannian manifold has the property that is preserves the ``kinetic energy'' associated with the metric. However, there are other affine connections which have this property, and ... 
An example with interesting controllability and stabilisation properties
Hirschorn, Ron M.; Lewis, Andrew D. (2005)A simple threestate system with two inputs is considered. The system's controllability is determined using properties of vectorvalued quadratic forms. The quadratic structure is then used as the basis for the design of ... 
Geometric local controllability: secondorder conditions
Hirschorn, Ron M.; Lewis, Andrew D. (2002)In a geometric point of view, a nonlinear control system, affine in the controls, is thought of as an affine subbundle of the tangent bundle of the state space. In deriving conditions for local controllability from ... 
Geometric sliding mode control: The linear and linearised theory
Hirschorn, Ron M.; Lewis, Andrew D. (2002)The idea of sliding mode control for stabilisation is investigated to determine its geometric features. A geometric definition is provided for a sliding submanifold, and for various properties of a sliding submanifold. Sliding ... 
The geometry of the GibbsAppell equations and Gauss's Principle of Least Constraint
Lewis, Andrew D. (1995)We present a generalisation of the GibbsAppell equations which is valid for general Lagrangians. The general form of the GibbsAppell equations is shown to be valid in the case when constraints and external forces ... 
The geometry of the maximum principle for affine connection control systems
Lewis, Andrew D. (2000)The maximum principle of Pontryagin is applied to systems where the drift vector field is the geodesic spray corresponding to an affine connection. The result is a secondorder differential equation whose righthand side ... 
Group structures in a class of control systems
Lewis, Andrew D. (1992)We investigate two classes of control systems, one of Brockett and one of Murray and Sastry. We are able to show that these two systems may be formulated in the language of principle fibre bundles. Controllability of ... 
Highorder variations for families of vector fields
Hirschorn, Ron M.; Lewis, Andrew D. (2002)Sufficient conditions involving Lie brackets of arbitrarily highorder are obtained for local controllability of families of vector fields. After providing a general framework for the generation of highorder ... 
Jacobian linearisation in a geometric setting
Lewis, Andrew D.; Tyner, David R. (IEEE, 2003)Linearisation is a common technique in control applications, putting useful analysis and design methodologies at the disposal of the control engineer. In this paper, linearisation is studied from a differential ... 
Kinematic controllability and motion planning for the snakeboard
Bullo, Francesco; Lewis, Andrew D. (IEEE, 2003)The snakeboard is shown to be kinematically controllable. Associated with the two decoupling vector fields for the problem, a constrained static nonlinear programming problem is posed whose solutions provide a solution to ... 
Lagrangian submanifolds and an application to the reduced Schrödinger equation in central force problems
Lewis, Andrew D. (D. Reidel, 1992)In this Letter, a Lagrangian foliation of the zero energy level is constructed for a family of planar central force problems. The dynamics on the leaves are explicitly computed and these dynamics are given a simple ...